Math Background

Data and Graphs: When Students Ask

  • Why should I bother learning this?
    Data and graphs are all around, and they report information on many aspects of real life. From the beginning of the unit make sure to show students real-world examples of the content. Engage them in looking for and sharing examples.
  • What's the difference between a bar graph and a histogram?
    The two kinds of displays look a lot alike. However, bar graphs show data for single categories or numbers. Histograms show interval data—that is, data grouped within a range of numbers such as 1−5, 6−10, 11−15, 16−20, and so on.
  • How can a line plot help me organize data?
    A line plot uses a number line and shows Xs for each value. It gives you a quick picture of the range of the data—how far it is spread out. You can pick out the mode or modes of a set of data by looking at the Xs and seeing which column or columns are the highest. You can see approximately where the middle of the data—the median—is by looking at the Xs. If you count the number of Xs and divide by 2 to find the middle one, then you can easily locate the median. For example, if there are 11 values, the middle value would be the sixth one. Another way to find the median is to count in from each end and meet at the median, or middle number.
  • When do I want to know the mode? The median? The mean?
    The mode is the most frequently occurring value in a set of data, so if you want to know a favorite choice, or most-often-chosen value, look for the mode. For example, a shoe store manager keeps track of sizes sold and based on this data, orders more shoes. Perhaps a mode is size 8. If so, the manager might order more size 8s than 4s or 10s.

    The median is the middle value. You can remember its name by thinking of the middle of road. The median tells us a typical value and is not affected by “outliers” or not-so typical values. For example, in the data set below 105 is the median. It is representative of the numbers in the set.

    1, 23, 100, 100, 105, 107, 108, 112, 599

    The mean is the average. When each number in a data set is of equal weight, the mean tells us a typical value. Suppose these were your test scores:

    85, 73, 100, 89, 97, and 90

    Each test score counted the same. You would add the numbers and divide by 6—the number of tests. The mean would be 89.

  • When should I use a double bar graph?
    Use a double bar graph when you are interested in two groups' data on the same topic. If you wanted to compare students in two grades, for example, you might use a double bar graph to show the responses of fifth graders and eighth graders. You might use double bar graphs to compare the responses or choices of boys and girls or children and adults.
  • When should I use a line graph?
    Line graphs are appropriate for data that shows change over time. The time might be minutes, days, weeks, years, or even longer periods of time, such as centuries. Time is usually shown on the horizontal axis. Then we can see the “ups and downs” of data for prices, numbers of people, or temperature on the vertical axis.
  • How is a line graph different from a bar graph?
    Line graphs are almost always used to show change of one or two factors over time. Bar graphs show numbers of separate factors. Their names also tell us something about the graphs: Line graphs use broken lines to show how data varies. Bar graphs use bars or rectangles to let us compare numbers.

Houghton Mifflin Math Grade 5